getwd()
## [1] "C:/Users/aldai/Documents"
setwd("D:/Documentos/Estadistica_Computacional")
library(plotly)
## Loading required package: ggplot2
##
## Attaching package: 'plotly'
## The following object is masked from 'package:ggplot2':
##
## last_plot
## The following object is masked from 'package:stats':
##
## filter
## The following object is masked from 'package:graphics':
##
## layout
library(VGAM)
## Loading required package: stats4
## Loading required package: splines
library(STAR)
## Loading required package: survival
## Loading required package: mgcv
## Loading required package: nlme
## This is mgcv 1.8-36. For overview type 'help("mgcv-package")'.
##
## Attaching package: 'mgcv'
## The following object is masked from 'package:VGAM':
##
## s
## Loading required package: R2HTML
## Loading required package: gss
## Loading required package: codetools
\[ f_{x}(x)=\frac{1}{2a} e^{\frac{-|x|}{a}} \mathbb{I}_{(-\infty, \infty)}(x), a>0\]
genexp <- function(x,a){
exp(-abs(x)/a)/(2*a)
}
x <- seq(-10,10,0.01)
data <- data.frame(x,genexp(x,1))
graph <- plot_ly(data, x= ~x, y= ~genexp(x,1), type= 'scatter', mode = 'lines')
layout(p=graph, title= "LAPLACE ", colorway= "Blue", yaxis=list(title= "fx"))
exp_ale <- function(a){
u_1 <- runif(1)
u_2 <- runif(1)
if(u_1<0.5){
return(-a*log(u_2))
} else {
return(a*log(u_2))
}
}
dexp <- as.numeric(list())
for(i in 1:5000){
dexp[i] <- exp_ale(1)
}
hist(dexp, col=rainbow(10), main="Distribución Laplace Simulada ", xlab="M.Gen", ylab="Probabilidad", ylim = c(0,0.5), ,probability = T)
lines(x, genexp(x,1), col="coral2", lwd=3)
#help(ks.test)
ks.test(dexp, plaplace(5000,0,1))
##
## Two-sample Kolmogorov-Smirnov test
##
## data: dexp and plaplace(5000, 0, 1)
## D = 0.8178, p-value = 0.3647
## alternative hypothesis: two-sided
El estradístico \(p\) mayor a 0.05 demuestra que no hay evidencia para rechazar la hipótesis. La muestra sí se distribuye como una Doble Exponencial.